simplify 6ln(13/9)

Solution

simplify

6 ln (\frac{13}{9})

6 (ln (13) - 2 ln (3))

Decimal Notation

2.20634 \dots

Solution steps

6 ln (\frac{13}{9})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{13}{9}) = ln (13) - ln (9)

= 6 (ln (13) - ln (9))

ln (9) = 2 ln (3)

= 6 (ln (13) - 2 ln (3))

14.307 ln (\frac{396.5}{303}) - 4.124 ln (3)

ln (\frac{58387}{88})

- \frac{1}{2} ln ∣ x ∣ + ln ∣ y ∣

- lo g_{10} (4.9 \cdot 1 0^{- 10} \cdot 0.1)

\frac{1}{75} ln (\frac{1}{12})